Master 3D Vectors: From Pythagoras to Vector Angles ⇢ 1.3 & 1.4 from Classical Mechanics

⍟ 𝐀𝐛𝐨𝐮𝐭 𝐓𝐡𝐢𝐬 𝐕𝐢𝐝𝐞𝐨 ⍟
Jump into the intricate realm of three-dimensional vectors as we elucidate the geometric intuition underlying the dot product. This comprehensive analysis dissects two pivotal problems from a classical mechanics textbook, illustrating the extension of the Pythagorean theorem to three-dimensional space and demonstrating the dot product's utility in determining the angle between vectors. This rigorous exploration is designed to enhance vector manipulation proficiency and deepen comprehension of fundamental concepts essential to mechanics, making it an invaluable resource for physics students and enthusiasts seeking to refine their analytical skills.

• 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜:
00:00 - Intro & Background.
00:15 - Problem Statements.
01:57 - Problem 1.3.
06:58 - Problem 1.4.
08:46 - Concluding Remarks.
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⍟ 𝐒𝐮𝐩𝐩𝐨𝐫𝐭 𝐓𝐡𝐢𝐬 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 ⍟
• ▶️ 𝘚𝘶𝘣𝘴𝘤𝘳𝘪𝘣𝘦 ▶️ ➜ http://tinyurl.com/4kd8wahb
• 🔎 𝘗𝘢𝘵𝘳𝘦𝘰𝘯 🔍 ➜   / curiousaboutscience  
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⍟ 𝐂𝐫𝐞𝐝𝐢𝐭𝐬/𝐑𝐞𝐬𝐨𝐮𝐫𝐜𝐞𝐬 ⍟
☞📚📖📓= Taylor, John R. “Newton’s Laws of Motion.” 𝘊𝘭𝘢𝘴𝘴𝘪𝘤𝘢𝘭 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘤𝘴, University Science Books, 2005, pp. 3–41.
• 3D Pythagorean Theorem: https://www.mathsisfun.com/geometry/p...
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⍟ 𝐌𝐢𝐬𝐬𝐢𝐨𝐧 ⍟
Science is a phenomenal exploration of nature. We hope to hone our skills of problem solving by exposing ourselves to multiple contexts. In doing so, it can sometimes be challenging to see the connection between topics. I yearn to understand 𝙝𝙤𝙬 these aspects of physics, unite together. To accomplish this, I'll cover all of my old textbooks through QFT; the convergence point of the many modern scientists! These posts are very much in a "𝘯𝘰𝘵𝘦𝘴 𝘵𝘰 𝘴𝘦𝘭𝘧" style. 𝙈𝙮 𝙝𝙤𝙥𝙚 is that by sharing this exploration, I can help others navigate the beautiful world of mathematics & physics through problems and examples, connecting the mathematical tools to their physical ramifications.

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